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LONDON — It was a wrong-place, wrong-time brush with danger: Protesting students — some chanting “Off with their heads!’’ — attacked Prince Charles and his wife, Camilla, as they rode in their vintage Rolls-Royce to a charity event at a London theater.

How could the mob have gotten so close, so easily, to the son of the queen?

There was no quick answer yesterday, amid criticism from security experts and calls for officials to be fired.

The royal couple was unharmed but visibly shaken Thursday after the angry protesters, pumped up by earlier scuffles with police, surrounded their limo, smashing a rear window and splashing it with white paint.

Video and photos from the Associated Press captured it all: Camilla, her mouth wide in horror, grasping for Charles as the rowdy crowd pummeled the car. Both were in full evening dress, Camilla’s glittering emerald and diamond necklace nestled against the green satin ruffle of her coat.

Buckingham Palace does not comment on royal security procedures, but security experts identified a host of failures surrounding the royal outing — and warned that procedures must be dramatically improved before Prince William’s wedding to Kate Middleton at Westminster Abbey this spring.

“It wasn’t potentially dangerous — it was dangerous,’’ said security analyst Charles Shoebridge, who called the attack “one of the most serious security breaches of the past decade.’’

He said the royal couple should have taken a different route to the theater, or waited until the streets were safe and clear of protesters, or simply sent their regrets and canceled.

“The best means of preventing a subject being attacked is to keep him out of harm’s way in the first place,’’ he said.

British police should have been talking with the royal protection squad to ensure the couple never came near the protests — and most certainly not in a 1977 Rolls-Royce, said Alex Bomberg, a former aide to the royal family and now chief executive of a private security firm.

The prince’s oversized luxury car lacked speed and maneuverability, and its large, clear windows — with reinforced but not bulletproof glass — meant Charles and Camilla were clearly visible inside.

With two police motorcycles in front and an official royal Jaguar behind it, the vehicle was instantly recognizable as a royal car.

“You couldn’t get away in an emergency in a vintage 1977 Rolls-Royce,’’ Bomberg said. “They should have used something more high-powered and up-to-date.’’

Protesters also got between the police escort and the royal car.

London’s theater district is a maze of narrow one-way streets and constantly crowded with tourists and theatergoers.

Cars and taxis making their way through the area often crawl at a snail’s pace — providing an easy target even for attackers on foot.

Without a clear escape route, the vehicle and route should never have been used, Bomberg said.

“You can’t blame the royal protection squad for a bunch of anarchists’ bad behavior,’’ Bomberg said. “But you can blame someone for not doing their job correctly and not understanding the situation as it was unfolding. Someone’s head should bloody roll.’’

Police, using live video feeds, should have kept the royal protection squad appraised of the volatile situation and been ready to change plans at a moment’s notice, Bomberg said.

Metropolitan Police Chief Paul Stephenson said the route was checked in advance, “including up to several minutes beforehand, when the route was still clear.’’

“I do think that the officers who were protecting their royal highnesses showed very real restraint. Some of those officers were armed,’’ he said.

Police would not comment on how close armed royal protection officers came to drawing their guns.